Ummm... You need to re-read the Constitution if you think the court ruling on a warrant is "disingenuous and illogical". The courts are simply following the Constitution you deride them for not following. BTW, it is the 4th that concerns this more than the 5th although they do go hand-in-hand most of the time.
No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.
You are referring to the part "nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law;" It is the court that dispenses due process of law. So encryption would most certainly block that due process.
Lastly, there are remedies to compel a suspect to comply with court orders to include imprisonment for contempt of court. Many have gone to jail for not complying with a legally issued court order to divulge their encryption password. So I don't see what this FBI Chief's issue is. He is using the age old "ticking time bomb" argument that was used to justify torturing detainees in Guantanamo. I don't buy it.